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8/2/2019 SSG 516 Mechanics of Continua 3
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@saf{ Ldefobsdnbh ]{`}f{sdf~Hfnsv{f Sa{ff
Ldefobsdn~7 ^svct `j Cd~}hbnfofes~ * O`sd`e
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saf {`sbsd`e bec saf nabeif de hfeisa `j bet jdk{f `j obsf{dbh
fobebsdei j{`o sabs }`des%
FA CdhhAfh}jvh [fbcdei7 K`yf{ }} 2>/>1( Jbldehfcf 23:/299
8/2/2019 SSG 516 Mechanics of Continua 3
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ldefobsdnbh }{`}f{sdf~
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8/2/2019 SSG 516 Mechanics of Continua 3
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d~ saf {bsd` `j saf hfeisa `j be
fhfofes de saf cfj`{ofc ~sbsf s` saf hfeisa `j saf ~bof
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8/2/2019 SSG 516 Mechanics of Continua 3
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8/2/2019 SSG 516 Mechanics of Continua 3
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8/2/2019 SSG 516 Mechanics of Continua 3
6/20
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8/2/2019 SSG 516 Mechanics of Continua 3
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N`e~dcf{ e`y sy` jdkf{~ sabs yf{f dedsdbhhtbs {dias beihf~%
Bjsf{ cfj`{obsd`e( hfs saf {dias beihf kfcfn{fb~fc kt
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n`~ ~de
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^afb{ ^s{bde
8/2/2019 SSG 516 Mechanics of Continua 3
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Saf i{fbs do}`{sbenf `j saf [dias Nbvnat/I{ffesfe~`{ de cfsf{odedei saf do}`{sbes ldefobsdnbhrvbesdsdf~ d~ nhfb{ j{`o saf j`{fi`dei% De saf efqs jfy
~hdcf~ yf ydhh sblf b nh`~f{ h``l bs ~`of `saf{ `j ds~}{`}f{sdf~%
]`hb{ cfn`o}`~dsd`e saf`{fo nbe kf besdnd}bsfc ktsaf j`hh`ydei }at~dnbh `k~f{zbsd`e7 Saf jdebh ~sbsf `jsaf cfj`{ofc nvkf ~a`ye kfh`y nbe kf bnadfzfc desy` cdjjf{fes ybt~7 B cfj`{obsd`e j`hh`yfc kt b{`sbsd`e( `{ b {`sbsd`e j`hh`yfc kt b cfj`{obsd`e b~saf cdbi{bo !Ydld}fcdb$ ~a`y~7
Saf ]`hb{ Cfn`o}`~dsd`e
8/2/2019 SSG 516 Mechanics of Continua 3
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]`hb{ Cfn`o}`~dsd`e
8/2/2019 SSG 516 Mechanics of Continua 3
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Yf ~sbsf( ydsa`vs }{``j( saf j`hh`ydei do}`{sbes {f~vhs7
J`{ b idzfe cfj`{obsd`e i{bcdfes( saf{f d~ b vedrvf{`sbsd`e sfe~`{( bec vedrvf( }`~dsdzf cfjdedsf ~toofs{dnsfe~`{~ bec j`{ yadna( bec bk`zf b{f nbhhfc saf {dias bec hfjs ~s{fsna
sfe~`{~ {f~}fnsdzfht% Nhfb{ht(
bec
]`hb{ Cfn`o}`~dsd`e Saf`{fo
8/2/2019 SSG 516 Mechanics of Continua 3
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[fnbhh sabs saf ~s{fsna {bsd` d~ cfjdefc b~7
Yadna bhh`y~ v~ s` y{dsf sabs( saf ~s{fsna bh`ei b veds zfns`{
( d~ Vo
Saf ^s{fsna Sfe~`{~
8/2/2019 SSG 516 Mechanics of Continua 3
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[fnbhh sabs saf ~s{fsna sfe~`{~ becb{f ~toofs{dn bec}`~dsdzf cfjdedsf% Ds j`hh`y~ sabs saf {dias Nbvnat/I{ffe
Sfe~`{ d~ bh~` ~toofs{dn bec }`~dsdzf cfjdedsf%Saf ^}fns{bh Cfn`o}`~dsd`e Saf`{fo7
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Yaf{f d~ saf fdifezbhvf n`{{f~}`ecdei s` ( 2 >
Saf ^}fns{bh Cfn`o}`~dsd`e
8/2/2019 SSG 516 Mechanics of Continua 3
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Saf ~}fns{bh cfn`o}`~dsd`e ~a`ye fb{hdf{ d~ vedrvf`eht yafe saf fdifezbhvf~ b{f cd~sdens% Sy` `saf{nb~f~7
7 [fnbhh sabs saf dcfesdst sfe~`{
~` sabs De sad~ nb~fsaf{fj`{f(
? Bec j`{ (
Frvbh {``s~
8/2/2019 SSG 516 Mechanics of Continua 3
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Hfs ( kf saf fdifezbhvf~ `j saf {dias ~s{fsna sfe~`{ !saf~f b{f bh~` nbhhfc saf }{dend}bh ~s{fsnaf~$ bec hfs( kf saf n`{{f~}`ecdei fdifezfns`{~( Saf ~}fns{bhsaf`{fo do}hdf~ sabs(
B cd{fns }{`cvns `j sad~ ydsa ds~fhj hfbc~ doofcdbsfht s`
^` sabs saf fdifezbhvf~ `j saf [dias Nbvnat/I{ffe Sfe~`{ b{fsaf ~rvb{f~ `j sa`~f `j saf [dias ^s{fsna sfe~`{%
Saf [dias ^s{fsna Sfe~`{
8/2/2019 SSG 516 Mechanics of Continua 3
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B Sfe~`{ d~ ~bdc s` kf {`sbsfc yafe ds d~ }{fovhsd}hdfc kt b {`sbsd`e bec }`~sovhsd}hdfc kt ds~ s{be~}`~f% Yf ~a`y de saf j`hh`ydei saf do}`{sbes jbns sabssad~ `}f{bsd`e c`f~ e`s bjjfns saf ~nbhb{ dezb{dbes~ `j b sfe~`{7
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saf sfe~`{% Yf vsdhdwf sad~ {f~vhs de saf j`hh`ydei cfcvnsd`e~%
]{dend}bh Dezb{dbes~ de [`sbsd`e
8/2/2019 SSG 516 Mechanics of Continua 3
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@k~f{zdei sabs ds d~ fb~dht~ffe sabs saf fdifezbhvf~ b{f }{f~f{zfc kt saf{`sbsd`e `j b sfe~`{% Afenf ( b{f bh~`fdifezbhvf~ `j % A`yfzf{ fdifezfns`{~ b{f cdjjf{feskfnbv~f `j saf {`sbsd`e~% De jbns( S S S
Yaf{f 2(;(>%Bec saf Hfjs Nbvnat/I{ffe Sfe~`{ ~ab{f~ saf~ffdifezfns`{~ ydsa ~rvb{f fdifezbhvf~ b~ fq}fnsfc7
Saf Hfjs ^s{fsna Sfe~`{
8/2/2019 SSG 516 Mechanics of Continua 3
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J`{ be fhfofes `j b{fb de saf cfj`{ofc k`ct ydsa bzfns`{ }{`gfnsdei `vs `j ds~ }hbef !c`f~ e`s abzf s` kfe`{obh s` ds$ yf abzf saf j`hh`ydei {fhbsd`e~ad}7 yaf{f
d~ saf fhfofes `j b{fb sabs s{be~j`{ofc s`
bec
d~ saf dobif `j de saf vecfj`{ofc obsf{dbh% E`sdei sabs( yf abzf(
Cdhbsbsd`e bec B{fb Nabeif~
8/2/2019 SSG 516 Mechanics of Continua 3
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~` sabs( Sad~ d~ Ebe~`e~ j`{ovhb j`{ `ksbdedei saf s{be~j`{ofc
b{fb kb~fc `e b idzfe b{fb fhfofes de saf vecfj`{ofck`ct%
Yf abzf ~ffe fb{hdf{ sabs saf z`hvof {bsd`( cfs
Ebe~`e~ J`{ovhb
8/2/2019 SSG 516 Mechanics of Continua 3
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8/2/2019 SSG 516 Mechanics of Continua 3
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>% V~f saf Nbthft/Abodhs`e saf`{fo s` ~a`y sabs(
b$ s{ ; k$ ; n$ cfs cfs cfs
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